The Portuguese defender put the Saints in front with just four minutes played when he flicked a corner from Adam Lallana into the net.
Fulham came out for the second half with a greater attacking threat and almost levelled up proceedings when Steve Sidwell struck the post from close range.
It then looked as though the visiting Londoners had stolen all three points as substitute Kieran Richardson sent the ball into the Southampton goal via a deflection off Hooiveld with just two minutes left.
However, from their very next attack, Southampton restored parity when Fonte flicked a cross from David Fox into the net.
The Saints looked the more likely to claim the victory during stoppage time but they were unable to score a third goal.